Define $f(x,y)= \frac{x^2y}{x^2 + y^2}$ if $(x,y)≠(0,0)$ and $f(x,y)=0$ if $(x,y)=(0,0)$. Determine if $f$ is differentiable at $(0,0)$.
Using limits and converting to polar coordinates, I determined that $f$ is continuous at $(0,0)$.
I also got that the partial derivatives exist and are constant functions both equal to $0$. But how do I determine from this if $f$ is differentiable at $(0, 0)$, step by step if possible?
